Numerical implementation of relativistic electromagnetic boundary conditions in a laboratory-frame grid

A new method for modeling moving, perfectly conducting surfaces is analyzed using a numerical technique based on the finite-difference time domain (FD-TD) method. Contrary to any other method, the numerical technique used does not require a system transformation where the object is at rest but gives a solution to the problem directly in the laboratory frame. The central idea of this new technique is the direct finite difference implementation of the relativistic boundary conditions at a moving surface. The electromagnetic wave scattering properties of a uniformly moving and vibrating rectangular cylinder are analyzed, first in one dimension and then in two dimensions. Results obtained are in excellent agreement with published analytical results. The new approach provides a method to analyze different problems of moving perfectly conducting scatterers where alternative analytical means are not available. Moreover, the time evolution of the fields are directly observable in the laboratory frame.